Underground Mathematics Insures Historical Buildings' Safety in Seville

November 30, 2009

Mathematicians from the University of Seville have suggested a way to design their city's next underground subway line that preserves the integrity of historical structures and monuments above ground.

"The methodology applied seeks to minimize the length of underground lines--with the subsequent economic saving--and to maximize their distance from historic buildings to avoid their being damaged," said Francisco A. Ortega. The researchers' mathematical design centers on "Voronoi diagrams," which divide planes into polygons created around points in such a way that their perimeters are equidistant from neighboring points. Their algorithm determines the shortest routes between two nodes of the Voronoi diagram while guaranteeing a safe distance from monuments; polygon edges are rounded to make routes smoother.

The study deals with the construction of line 2 of the Seville underground, which will link the city's Palacio de Congresos (Conference Center) with Santa Justa railway station, the historic center, and the district of Triana. Because seventy-two historic buildings would be impacted by the construction, the method provides "genuine, feasible and efficient solutions" for the line. Leaving an average safety radius of 80 meters around historic buildings and sites, the work also suggests non-disruptive alternatives for the underground construction.

Ortega noted that "There have been doubts as to the viability of this work regarding the safety of nearby buildings due to previous experiences, such as the fact that the construction of the first underground line in Seville in the seventies was suspended out of fear that the cathedral might be affected, or more recently in the district of Carmel, Barcelona, where the structure of certain buildings was damaged as a result of the works carried out to extend the underground."

G. Laporte, J. A. Mesa, and M.A. Pozo also collaborated on the research paper, titled “Locating a Metro Line in a Historical City Center: Application to Seville," which appeared in the Journal of the Operational Research Society (October, 2009).

Source: SINC, November 10, 2009.